Thickness Of Transition Layer Research Articles

Head waves from a transition layer

abstract Ultrasonic, seismic-model experiments have been performed to re-examine the nature of head waves from a transition layer. Two-dimensional, layered structures, some with a transition zone and some with a sharp discontinuity, constructed by lead-aluminum laminations have served as the models. Amplitude and phase responses have been measured in a frequency range of 25 kHz to 200 kHz. At low frequencies, where the wavelength is much longer than the thickness of the transition zone, little difference is observed between head waves from a transition zone and those from a sharp discontinuity. At a certain frequency range where the wavelength is close to the thickness of the transition zone, the measured head-wave amplitude from a transition zone becomes a few times larger than that from a sharp discontinuity. This is characteristic of head waves from a poorly defined boundary and may be used to estimate the thickness of a general transition layer. A sharp, high-frequency cutoff is again observed, but the cutoff frequency is not consistent with previous studies.

Analysis of the Transition Region between a Uniform Plasma and its Confining Magnetic Field. II

The case of one-dimensional geometry for the transition region separating a uniform plasma from its confining magnetic field is considered. The magnetic-field profile within the boundary layer is determined by the current distribution, i.e., by the paths of the ions and electrons. The paths of these particles, on the other hand, are determined by the fields in which they move. An exact, self-consistent solution of Maxwell's equations and the equations of motion of the particles is obtained. A detailed analysis is made for a hydrogen plasma. These results are then compared with those of a plasma whose positive constituent is the proton and whose negative constituent has a mass which approaches zero and a speed which approaches infinity in such a way that the energy remains finite. The transition layer thickness for these two plasmas agree to one part in 106. It is shown that this latter case is equivalent to treating the electrons of the hydrogen plasma in the guiding-center approximation.

Self-Consistent Field and Motion of Electrons Which Have a Range in Canonical Angular Momentum in a Uniform Magnetic Field

The self-consistent theory of relativistic electrons circulating in a uniform impressed magnetic field, the "Astron problem," has been generalized to the extent that a range of canonical angular momentum among monoenergetic electrons has been treated. For simplicity, the density distribution in phase space has been chosen to be uniform over a finite momentum range. Just as in the single-momentum case, field reversal is found, but new field and spatial density configurations appear. The uniform distribution is found to be consistent with isotropic regions of constant spatial density and constant magnetic field. The thickness of transition layer between vacuum and such a region conforms, within limits, to an empirical relation previously found. The limit to the number of electrons per unit axial length of layer still exists. The curves relating the ratio of internal to external field to the layer strength still show multiple values of both ratio and strength in certain ranges. Trajectories have been calculated and plotted for several cases.

Interaction of the Solar Wind with the Geomagnetic Field

The dynamical properties of the solar wind blowing past the geomagnetic field are investigated by considering the effective viscosity and the resulting transition layer thickness. The collision of ions in the solar wind produces a negligible viscosity in the flow past the geomagnetic field, but such an inviscid flow is shown to be unstable. The resulting disordered interface between the field and the wind yields Fermi acceleration of ions and consequently a not insignificant effective viscosity. The Fermi acceleration results in suprathermal ions which may have an energy spectrum like that observed for primary auroral protons. The auroral zones and the agitated nature of the polar geomagnetic field are shown to follow from the depth of penetration of the solar wind into the geomagnetic field. The injection of gas into the geomagnetic field is studied. The effect at Earth of the distortion of the outer boundary of the geomagnetic field is computed; no matter how unevenly and anisotropically the outer field is distorted, the effect at Earth is a nearly uniform perturbation field which is closely parallel to the geomagnetic axis. Pushing in on the outer field increases the horizontal component at Earth, and pulling out decreases it; the total increase of the horizontal component is the algebraic sum of all the pushing and pulling. The simultaneous world-wide onset and the main phase of a geomagnetic storm follow. The common tendency of large and/or violent bodies of plasma to produce suprathermal particles is noted and suggested to be a general dynamical property.

Reflection of Sound in the Ocean from Temperature Changes

When the temperature of the ocean changes with depth within a horizontal layer, it is accompanied by a change in the velocity of sound. The reflection of sound from such a transition layer depends on the incident angle and wavelength of the sound, the thickness of the layer, the manner in which the velocity changes, and the total amount of the change. The usual formula for reflection assumes a transition layer of negligible thickness. The reflection coefficient then depends only on the incident angle and the total velocity change. This case is treated and numerical values are given for the reflection coefficient under conditions of practical interest. It is then shown that for a gradual velocity change which corresponds to certain temperature data, the reflection coefficient for small glancing angles of incidence changes gradually with increasing layer thickness and may be approximated very closely by the usual formula. Quantitative comparison of the cases is made and the general applicability of the approximation is discussed.